Double decimation and sliding vacua in the nuclear many-body system

Abstract

We propose that effective field theories for nuclei and nuclear matter comprise of "double decimation": (1) the chiral symmetry decimation (CSD) and (2) Fermi liquid decimation (FLD). The Brown-Rho scaling identified as the parametric dependence intrinsic in the "vector manifestation" of hidden local symmetry theory of Harada and Yamawaki results from the first decimation, i.e., CSD. In a recent work we showed that in matter under conditions of high density or high temperature, dynamically generated hadron masses scaled with a common scale. Namely for low densities and temperatures the masses scaled as m ⋆ /m ≃ [ qq ⋆ / qq ] 1/2 whereas at higher densities and temperatures as [ qq ⋆ / qq ]. In the present work we summarize new empirical evidence for Brown-Rho (BR) scaling and discuss in a general way its impact on the nuclear many-body problem. While the double decimation should be carried out, it has been a prevalent practice in nuclear physics community to proceed with the second decimation, assuming density independent masses, without implementing the first, chiral symmetry decimation. We show why most nuclear phenomena can be reproduced by theories using either densityindependent, or density-dependent masses, a grand conspiracy of nature that is an aspect that could be tied to the Cheshire-Cat phenomenon in hadron physics. We go through some of the history of the chiral symmetry decimation (CSD) which involves BR scaling, in order to show that historically one had to look at very specific phenomena involving transition matrix elements to see that it is necessary. We identify what is left out in the Fermi liquid decimation (FLD) that does not incorporate the CSD. Experiments such as the dilepton production in relativistic heavy ion reactions, which are specifically designed to observe effects of dropping masses, could exhibit large effects from the reduced masses. However they are compounded with effects that are not directly tied to chiral symmetry. We discuss a recent STAR/RHIC observation where BR scaling can be singled out in a pristine environment.1 The holes are on-shell in the Brueckner-Bethe theory. 2 We are assuming U (2) flavor symmetry in the two-flavor case. 3 Implementing temperature effects is straightforward and hence will be ignored in what follows in this section. 11 In HLS/VM with the explicit vector degrees of freedom, the scaling parameters are the gauge coupling g * , the vector-meson mass m * V , the pion decay constant F * π and the coefficient a. However in medium a * ≈ 1, g * ≈ g, so mV * goes as F * π through HLS/VM relations. We are left with only one scaling factor as in the case where the vectors are integrated out. 12 The deviation from vector dominance in the photon coupling to the baryons has been known since some time. In fact, the chiral bag model [27, 68] provided a natural mechanism for such a deviation.

Spectral functions from the functional renormalization group

“…4 and displays the typical shape [24] found in quark-meson model calculations beyond the mean-field approximation with a critical endpoint at µ = 293 MeV and T = 10 MeV for this parameter set. 2 In addition, it is also instructive to consider the temperature-and chemical potential-dependence of the meson screening masses as they will be used to identify thresholds in the spectral functions, cf. We now turn to the discussion of results for the sigma and pion spectral functions, ρ σ (ω) and ρ π (ω).…”

“…The in-medium modifications of hadron properties have been dear to Gerry's heart and his work on this subject has made him and his collaborators major drivers of this field for several decades [1,2]. The discussions are far from over and we wish to pay tribute to Gerry's physical insights by adding a new and promising alternative for computing real-time spectral functions in hot and dense QCD matter.…”

On Effective Degrees of Freedom at Chiral Restoration and the Vector Manifestation

“…A variety of other evidences that lend, albeit indirect, support to the scaling 14 and in consequence to the notion of the VM are discussed in 23,20,24 . If the VM were verified by going near the chiral transition point, it would constitute a nice illustration of how the mass of the hadrons making up the bulk of ordinary matter around us is made to "disappear," a deep issue in physics 25 .…”

“…The double-decimation approximation is to simply assume that this relation holds from zero density up to nuclear matter density 20 . Note that we are essentially summarizing the phase structure up to chiral restoration by two fixed points, namely, the Fermi-liquid fixed point and the vector-manifestation fixed point.…”

In search of a pristine signal for (scale-)chiral symmetry in nuclei

“…It involves "double decimations" [21]. For nuclear processes, one should be able to do the decimation from a cutoffΛ somewhat lower than ρ mass.…”